320 al. 1995; Asner et al. 2002; Unger et al. 2014; Song et al. 2021). Measuring Tree Height Measuring tree height, including total tree height and live crown height, is important in urban forest inven- tories for calculating ecosystem services. For exam- ple, i-Tree Eco (USDA; Madison, WI, USA) uses tree height to estimate the energy effects that trees have on residential buildings (United States Forest Service 2021). In arboriculture and forestry operations, mea- suring tree height can help inform whether there is sufficient room to fell a tree. Being able to measure the tree felling radius with reasonable accuracy is imperative to safe operating procedures (Tree Care Industry Association 2014). There are numerous methods for measuring tree height, including nonelectronic methods (e.g., clinom- eters), handheld electronic measurement tools (ex., handheld laser rangefinders), and terrestrial, airborne, and mounted measurement equipment (ex., LiDAR) (Wing et al. 2004; Vastaranta et al. 2015). Examining the accuracy of methods is important as measure- ments of tree height often have significant error (Waguchi 2002). The stick method, which uses a straight stick and geometric principles to estimate tree height, is one of the most rudimentary methods of tree height mea- surements. In this study, “stick method” does not refer to the Biltmore stick—a purpose-built measur- ing tool for tree mensuration—but rather a more sim- plistic measurement method (Figure 1). The measurer uses a stick the length of their arm, holding the stick outright to form an isosceles triangle. Looking at the top of the tree “through” the top of the stick, the mea- surer walks toward or away from the tree until the tree’s top is at a point along length c consistent with the top of the stick. Measuring from the feet of the measurer to the base of the tree and adding the length y, the measurer is able to determine the tree height. While the use of the stick method has largely been omitted in formal urban forest inventories based on technological advances, the stick method is still used in arboriculture and logging operations for rapid tree height estimates without the need for expensive tree measurement tools. Given its use within arboriculture operations, it has been included within this study. Further, the need to instruct early career professionals and students in the foundational concepts and ©2022 International Society of Arboriculture Figure 1. Trigonometry of the stick method. Ls which is equal to La = length of stick, = length of arm. Length a, the distance from the eye of the measurer to the base of the tree, is equal to length b, the height from the eye of the measurer to the top of the tree. Length c denotes the hypotenuse of the isosceles right triangle, and y denotes the distance from the eye of the measurer to the ground. Martin: Accuracy and Precision of Tree Height Measurement Tools mensuration methodology is important in establish- ing a core understanding of urban forestry practices. Through expansion of the stick method’s simplis- tic geometric principles via trigonometric calcula- tions, the clinometer introduces more versatility. This is true because a 45° angle is not required to measure tree height with clinometers. However, the use of a clinometer still requires a measuring tape to deter- mine linear distance (the horizontal cathetus) for the trigonometric equation. By contrast, handheld electronic/laser rangefind- ers provide a more rapid measurement of tree height, as well as horizontal and angular measurements, without the need for supplemental tools (Wing et al. 2004). While electronic distance measurement tools were adopted into ranging and surveying use in the 1960s, it was only after the tools were made portable that they began to become popular in forestry appli- cations (Liu 1995). Over recent years, rangefinders have become increasingly affordable (Wing et al. 2004). A study by Wing et al. (2004) compared the accuracy of digital rangefinders, finding that some overestimated while others underestimated height; however, it should be noted that the rangefinders tested may have been updated since the study. A
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